%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:59 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 15 unt; 9 def)
% Number of atoms : 180 ( 38 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 193 ( 71 ~; 74 |; 33 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f48,plain,
aElement0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f79,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f80,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f184,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f185,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f184]) ).
fof(f186,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f185]) ).
fof(f187,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f186]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3)
| aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f197,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f198,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f203,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f204,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f229,definition,
( sQ2_spl
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f232,definition,
( sQ3_spl
<=> aElementOf0(xa,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f235,definition,
( sQ4_spl
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f238,definition,
( sQ5_spl
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f204,f229,f232,f235,f238]) ).
fof(f253,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f191]) ).
fof(f261,plain,
sdtasdt0(xb,sz00) = sz00,
inference(resolution,[status(thm)],[f80,f198]) ).
fof(f262,plain,
sdtasdt0(xa,sz00) = sz00,
inference(resolution,[status(thm)],[f80,f197]) ).
fof(f286,definition,
( sQ6_spl
<=> aElement0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ6_spl
| ~ aElement0(sz00) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f298,definition,
( sQ7_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ7_spl
| ~ aElement0(xa) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f303,definition,
( sQ8_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ8_spl
| ~ aElement0(xb) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f312,plain,
( ~ aElement0(sz00)
| aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(paramodulation,[status(thm)],[f261,f253]) ).
fof(f319,plain,
( ~ sQ6_spl
| sQ4_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f312,f303,f235,f286]) ).
fof(f322,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f48]) ).
fof(f323,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f198]) ).
fof(f325,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( ~ aElement0(sz00)
| aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(xa) ),
inference(paramodulation,[status(thm)],[f262,f253]) ).
fof(f331,plain,
( ~ sQ6_spl
| sQ2_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f327,f298,f229,f286]) ).
fof(f334,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f197]) ).
fof(f335,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f351,definition,
( sQ11_spl
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ11_spl
| ~ aElement0(sz10) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f364,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f49]) ).
fof(f365,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f448,plain,
sdtasdt0(xb,sz10) = xb,
inference(resolution,[status(thm)],[f71,f198]) ).
fof(f449,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolution,[status(thm)],[f71,f197]) ).
fof(f497,plain,
( ~ aElement0(sz10)
| aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(paramodulation,[status(thm)],[f448,f253]) ).
fof(f500,plain,
( ~ sQ11_spl
| sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f497,f303,f238,f351]) ).
fof(f510,plain,
( ~ aElement0(sz10)
| aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(xa) ),
inference(paramodulation,[status(thm)],[f449,f253]) ).
fof(f513,plain,
( ~ sQ11_spl
| sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f510,f298,f232,f351]) ).
fof(f516,plain,
$false,
inference(sat_refutation,[status(thm)],[f241,f319,f323,f325,f331,f335,f365,f500,f513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:20:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.053421 seconds
% 0.13/0.42 % CPU time: 0.160395 seconds
% 0.13/0.42 % Total memory used: 106.199 MB
% 0.13/0.42 % Net memory used: 106.039 MB
%------------------------------------------------------------------------------